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The RD Sharma Class 12 Chapter 3 Solutions are the best to buy. The chapters and exercises in RD Sharma Class 12 may be difficult for a student to grasp. They will find it easier with RD Sharma Class 12th Exercise 3.14. Students can now use these solutions to solve any Relationship problem. The questions and answers are written in a way that students can easily understand. These solutions lay the groundwork for students' understanding of mathematics. The concepts are now easily understood by the students.

Many students find mathematics a difficult subject. These solutions will make students happy because they will learn all of the concepts quickly and easily. With these solutions, the approach to learning and understanding topics will be forever altered. RD Sharma Solutions is here to ensure that every student excels in mathematics, so the book includes various tricks and tips.

- Chapter 3 - Inverse Trigonometric Ex 3.1
- Chapter 3 - Inverse Trigonometric Ex 3.2
- Chapter 3 - Inverse Trigonometric Ex 3.3
- Chapter 3 - Inverse Trigonometric Ex 3.4
- Chapter 3 - Inverse Trigonometric Ex 3.5
- Chapter 3 - Inverse Trigonometric Ex 3.6
- Chapter 3 - Inverse Trigonometric Ex 3.7
- Chapter 3 - Inverse Trigonometric Ex 3.8
- Chapter 3 - Inverse Trigonometric Ex 3.9
- Chapter 3 - Inverse Trigonometric Ex 3.10
- Chapter 3 - Inverse Trigonometric Ex 3.11
- Chapter 3 - Inverse Trigonometric Ex 3.12
- Chapter 3 - Inverse Trigonometric Ex 3.13
- Chapter 3 - Inverse Trigonometric Ex VSA

Inverse Trigonometric Functions Excercise: 3.14

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Download E-bookInverse Trigonometric Functions Exercise 3.14 Question 1(i)

Hints: First we will solve for and we use the formula

Let us first solve for

................(2)

Now, we know that

Now from equation (1), (2) and (3)

We get

Hints: First we will convert into

Let

In

(By using Pythagoras theorem)

Now

from equation (1)

Now,

from equation (2)

On rationalizing we get,

Hint: First we will convert into

Let

we know that

from equation (1)

......(2)

Now

from equation (2)

Hints: we will convert into and into

First we will solve for

We know that

.................(2)

Now Let .................(3)

By Pythagoras theorem:

from equation.........(2)

..................(4)

Now from equation (1)

Putting the value of and from equations (2) and (4) respectively

Hints: First we will convert into and after that we use the formula of

First we will solve for

let ........................(1)

By Pythagoras theorem

From Equation (1)

..............(2)

Now L.H.S:

from equation (2)

Hence

Inverse Trigonometric Functions Exercise 3.14 Question 2 sub question 2

Hints: First we will solve for then we will convert it into respectively.

First we will solve for

(On multiplying and dividing by 2)

.......................(1)

Now,let ....................(2)

from equation (2)

.........(3)

From equation (1) and (2) we get

Hint: First we will multiply in numerator and denominator by 2 in L.H.S so that we can use the formula of

L.H.S:

On multiply in numerator and denominator by 2.

Hence it is proved.

Inverse Trigonometric Functions Exercise 3.14 Question 2 sub question 4

Hints: First we will use the formula of .

L.H.S:

Hence it is proved that

Inverse Trigonometric Functions Exercise 3.14 Question 2 sub question 5

**Answer: **

Hints: First we will convert in **Given: ****Explanation: **

L.H.S:** **** **

Hence it is proved that

Hint: First we will convert into .

Let us solve for

Let ............(1)

Now,

From equation (1)

.............(2)

L.H.S:

from Equation (2)

Hence it is Prove that

Inverse Trigonometric Functions Exercise 3.14 Question 2 sub question 7 .**Answer:**

Hint: First we will solve for **Given: ****Explanation:**

L.H.S:

Hence it is proved that

Hint: First we will solve for **Given: ****Explanation:**

L.H.S:

Hence it is proved that

Hint: First we will solve for

L.H.S:

From equation (1)

Hence it is proved that

Inverse Trigonomeric Functions Exercise 3.14 Question 2 Sub Question 10.

Hints: First we will solve for

Split into and solve it

Now

L.H.S:

Hence it is proved that

Inverse Trigonomeric Functions Exercise 3.14 Question 3 .

Hints: First we will convert whole L.H.S part in

As we know that

Now

Hence it is proved that

Inverse Trigonomeric Functions Exercise 3.14 Question 4 Sub Question 1 .

Hint: First we will convert into

L.H.S:

Hence it is Proved that

Inverse Trigonomeric Functions Exercise 3.14 Question 4 Sub Question 2.

**Answer: **

Hint: First we will convert into **Given: ****Explanation:**

L.H.S:

Hence it is proved that

Hints: We will first convert into sin

Let

Now

Hence it is proved that

Hints: First we will convert L.H.S of the question in

Hence it is proved that

Inverse Trigonomeric Functions Exercise 3.14 Question 6.

**Answer: **

Hint: First we will convert into **Given: **for **Explanation:**** **

Let

Hence the constant value for is

Inverse Trigonomeric Functions Exercise 3.14 Question 7 Sub Question 1.

**Answer: **

Hint: First we solve Since

Solution: We have,

This is the required solution.

Inverse Trigonomeric Functions Exercise 3.14 Question 7 Sub Question 2.

**Answer:** 0**Given: **

Hint: Since applying it.

Solution: We have,

=0

Hence,

Inverse Trigonometric Function Exercise 3.14 Question 8 Sub Question 1.

Hint: Use formula

Solution: We have,

We know that

Hence is required answer

Inverse Trigonometric Function Exercise 3.14 Question 8 Sub Question 2.

Hint: Using formula since,

Solution: We have,

We know that

This is required solution.

Inverse Trigonometric Function Exercise 3.14 Question 8 Sub Question 3.

Hint: Use

Solution: We have,

We know that,

and convert into

Inverse Trigonometric Function Exercise 3.14 Question 8 Sub Question 4.

Hint: Using

Solution: We have,

We know that

Hence the principal value of

Inverse Trigonometric Function Exercise 3.14 Question 8 Sub Question 5.

Hint: Using formula

We have,

We know that,

Hence is required solution.

Inverse Trigonometric Function Exercise 3.14 Question 8 Sub Question 6.

Hint: Using formula

We have,

We know that,

Hence is required solution.

Inverse Trigonometric Function Exercise 3.14 Question 9.

**Answer: ****Given: **

Hint: Using

Solution: Let us assume

Dividing numerator and denominator by we get

Hence

Inverse Trigonometric Functions Exercise 3.14 Question 10.

Hint: Use

L.H.S:

We know that

Hence ,

Inverse Trigonomeric Functions Exercise 3.14 Question 11.

**Answer: ****Given**: For any a, b, x, y > 0

We have to prove that

where,

Hint: First we will divide numerator and denominator of first function and second function by and respectively, then use

Solution: Let us assume

Dividing numerator and denominator of first function and second function by and respectively.

We know that,

Hence, Where

RD Sharma Class 12 Solutions Chapter 3 Exercise 3.14 involves inverse trigonometric problems related to cosecant, secant, cosine, tangent functions. Solving these problems will make a student grasp better and perform well in exams.

In calculus, Inverse Trigonometric Functions are used to find various integrals. In addition to mathematics, inverse trigonometric functions are applied in science and engineering. Students will learn about the domain and range restrictions of trigonometric functions that ensure the existence of their inverses and how to observe their behavior using graphical representations and examples.

The specific exercise 3.14 has 31 questions, including subparts, and now a student can practice a lot and gain knowledge about the topic. In addition, this exercise will help in overall understanding of the chapter. RD Sharma Class 12 Solutions Chapter 3 Exercise 3.14 has practice questions which are to be solved and are important for exam point of view. The concepts are now easily understood by the students.

**Created by experts**

With these solutions, the approach to learning and understanding topics will be forever altered. RD Sharma Solutions is here that has been created by a team of experts to ensure that every student excels in mathematics, which is why the book includes a variety of tricks and tips.

**Best solutions for preparation**

RD Sharma Class 12 textbook has high-level questions which sometimes become difficult for a student to solve. The RD Sharma Class 12 Solutions makes it easy. The chapters and exercises are covered wonderfully to help students in every possible way.

Students can refer to these solutions to gain extra knowledge about the topics. It is advisable to solve the practice questions to avail the benefit of these solutions.

**NCERT based questions**

Students can refer to these solutions to gain extra knowledge about the topics. It is advisable to solve the practice questions to avail the benefit of these solutions. The questions are set from NCERT books as teachers consider it as a standard.The students must buy RD Sharma Class 12 Solutions Chapter 1 Ex 1.2 to score well in board exams.

**Different ways to solve a question**

As the team of experts format the solutions, there are many ways which come out to solve one question. A student gets benefit from this technique. Here the illustrated examples are also included to make the learning easy and clarify the concepts a priority.

**Free of cost**

Career360 provides these solutions free of cost, and every student must refer to these solutions to get the benefit. Therefore, students have a golden opportunity to learn and get a lot of knowledge from these solutions. Many students have availed of the opportunity given by Career360, and now it is your turn to grab the exciting offer. If still unsure, you can also visit the website and find more expert-created answers.

**Chapter-wise RD Sharma Class 12 Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Why should I refer to RD Sharma Class 12 Maths Book?

RD Sharma Class 12 Maths Book is the best book for preparation for any exam. This book will take you to your goal if you want to give competitive exams like IIT JEE. RD Sharma Class 12 Maths Solutions Chapter 3 Exercise 3.10 has everything like examples, tips, tricks, and practice questions to grab a hold on the subject.k

2. Are these solutions free of cost and updated?

Yes, the solutions by Career360 are free and updated with the latest questions of the book. You can avail the benefits by going to the website. The high quality of these solutions will increase the grasp on every topic.

3. What are the benefits of these solutions?

The solutions are beneficial for every student because of the easy language and explained topics. For example, RD Sharma Class 12 Maths Solutions Chapter 3 Exercise 3.5 has everything a student requires to score well and compete better in exams.

4. What are inverse trigonometric functions?

The inverse trigonometric functions of sine, cosine, tangent, cosecant, secant and cotangent are used to find the angle of a triangle from any of the trigonometric functions.

5. What are other uses of inverse trigonometric functions?

The inverse trigonometric functions are helpful in geometry, physics and engineering too.

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